MinT - Information on Result #1552204

Information on Result #1552204

Linear OOA(7⁷⁵, 235306, F₇, 3, 13) (dual of [(235306, 3), 705843, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(7⁷⁵, 235306, F₇, 13) (dual of [235306, 235231, 14]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(7⁷⁴, 235304, F₇, 13) (dual of [235304, 235230, 14]-code), using
  - trace code [i] based on linear OA(49³⁷, 117652, F₄₉, 13) (dual of [117652, 117615, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(49³⁷, 117649, F₄₉, 13) (dual of [117649, 117612, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(49³⁴, 117649, F₄₉, 12) (dual of [117649, 117615, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 117648Â = 49³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(49⁰, 3, F₄₉, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
2. linear OA(7⁷⁴, 235305, F₇, 12) (dual of [235305, 235231, 13]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁷⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 1 112582 733665 983148 887713 491969 761991 730743 514477 866661 927361 [i]
3. linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁷⁵, 117652, F₇, 15, 13) (dual of [(117652, 15), 1764705, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row